We present an implementation of the coherent dedispersion algorithm capable of dedispersing high-time-resolution radio observations to many different dispersion measures (DMs). This approach allows the removal of the dispersive effects of the interstellar medium and enables searches for pulsed emission from pulsars and other millisecond-duration transients at low observing frequencies and/or high DMs where time broadening of the signal due to dispersive smearing would otherwise severely reduce the sensitivity. The implementation, called 'cdmt', for Coherent Dispersion Measure Trials, exploits the parallel processing capability of general-purpose graphics processing units to accelerate the computations. We describe the coherent dedispersion algorithm and detail how cdmt implements the algorithm to efficiently compute many coherent DM trials. We present the concept of a semi-coherent dedispersion search, where coherently dedispersed trials at coarsely separated DMs are subsequently incoherently dedispersed at finer steps in DM. The software is used in an ongoing LOFAR pilot survey to test the feasibility of performing semi-coherent dedispersion searches for millisecond pulsars at 135MHz. This pilot survey has led to the discovery of a radio millisecond pulsar -- the first at these low frequencies. This is the first time that such a broad and comprehensive search in DM-space has been done using coherent dedispersion, and we argue that future low-frequency pulsar searches using this approach are both scientifically compelling and feasible. Finally, we compare the performance of cdmt with other available alternatives.
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